Origins of the concepts cause, cost, and goal in prereaching infants


Shari Liu

We began by replicating the finding that 3-month-old infants, who have received no sticky mittens training and are habituated to an actor reaching over a barrier, show no differential looking to efficient versus inefficient reaching actions after the barrier is removed (29). In Experiment 1, we tested for infants’ sensitivity to action efficiency using events based directly on past research (29), featuring reaches by an actor wearing a glove rather than a mitten (Figure 1). Three-month-old infants (N=20; Mean age=108 days; range=92-122, 11 female) viewed video clips of an actor who reached over a barrier, grasped and lifted a ball, and moved the ball to her side of the barrier (Figure 1A, H1). The height of this barrier varied across trials, and the person always adapted her reach to the barrier. After infants either habituated to these events (i.e. their attention declined by 50%), or looked for 12 trials, whichever came first, we measured their attention to alternating test events in which the person reached for the same ball as during habituation, but with no obstacles in her way (Figure 1B, T1). On alternating test trials, she reached on the same curvilinear path towards the ball (a familiar but newly inefficient action) or on a direct path (a novel but newly efficient action). The only differences between these events and the events from past studies (29) were that the actor in this study wore a tight-fitting white glove instead of a brown mitten, and she kept her hand in the same grasping position during the entire reach, instead of turning the ball over in the mitten after retrieving it. Thus, the shape and positions of her fingers remained visible throughout the action.

Across all experiments, we calculated the average looking time towards the efficient versus inefficient reach over 3 pairs of test events, and we analyzed these data using linear mixed effects models (44). For details about our analysis strategy, see Materials and Methods. In light of past findings that prereaching infants fail to interpret reaching actions by a mittened hand as costly (29), we expected infants to look equally at the two test events in Experiment 1. Consistent with this prediction, infants looked equally to the inefficient and the efficient reach of the gloved hand (Mineff=18.029s, Meff=16.844s, [-0.089,0.238], ß=0.155, B=0.074, SE=0.079, p=0.359, two-tailed). See Figure 2A. Nevertheless, looking preferences in this experiment differed marginally from those in the experiment on which this study was based (29), with relatively greater looking at the familiar but inefficient reach, ([-0.015,0.464], ß=0.43, B=0.224, SE=0.122, p=0.074, two-tailed).

Do 3-month-old infants struggle to represent the cost of mittened and gloved reaches because of the gloves and mittens themselves? In Experiment 2, infants (N=20; Mean age=108 days; range=93-120; 12 female) were presented with the same actions from Experiment 1, except that the person performing the actions wore no gloves, further clarifying the contact relation between her hand and the object (Figure 1, H2 and T2). Infants looked longer at the inefficient than the efficient reach of the bare hand, in the familiar context of a bare-handed reach (Mineff=9.715s, Meff=8.036s, [0.008,0.331], ß=0.429, B=0.17, SE=0.078, p=0.043, two-tailed). Performance in Experiment 2 differed significantly from performance in the original study on which it was based (29) ([0.047,0.547], ß=0.539, B=0.297, SE=0.124, p=0.022, two-tailed). However, performance in Experiments 1 and 2 did not differ from each other ([-0.128,0.319], ß=0.167, B=0.095, SE=0.111, p=0.396, two-tailed, excluding 3 influential participants). Collapsing across both Experiments 1 and 2, infants looked marginally longer at the inefficient than the efficient action (Mineff=13.872s, Meff=12.44s, [-0.004,0.227], ß=0.185, B=0.112, SE=0.058, p=0.06, two-tailed) (Figure 2).

These experiments, together with past research (28, 29), suggest that untrained 3-month-old infants have weak and inconsistent looking preferences for direct versus indirect reaching and grasping actions. Nevertheless, the significant difference between Experiment 2 and the experiment presenting a mittened hand (29) calls into question the conclusion, from past research, that 3-month-old infants need action training in order to appreciate the physical costs of reaching actions. An exploratory analysis comparing the three experiments that used this method revealed that the magnitude of infants’ looking preference for the indirect reach increased with increases in the visibility of the form of the reaching hand, from a mitten that obscured its shape and texture (29)), to a glove that revealed its shape but obscured its color and texture (Experiment 1), to a fully visible hand (Experiment 2) ([0.007,0.053], ß=0.416, B=0.03, SE=0.011, p=0.011, two-tailed). The SI Appendix presents a full report of this exploratory analysis, which raises the possibility that the use of mittens obscuring the hand in all past research with 3-month-old infants underestimates the infants’ sensitivity to natural, bare-handed acts of reaching. Further research is needed to test this possibility.

Overall, Experiments 1 and 2 cast doubt on the conclusion that prereaching infants are wholly insensitive to reaching actions that vary in efficiency, but they confirm past observations that young infants do not robustly represent acts of picking up and entraining an object as goal-directed and costly. What makes reaching for, grasping, and lifting objects problematic actions for 3-month-old infants? Although infants frequently see people lifting objects, the mechanism by which this action serves to displace an object depends on variables that are opaque to vision, such as the weight of the object and the force of the actor’s grasp. Without understanding how the posture of the hand and the forces it exerts allow an actor to lift and move an object, infants may have difficulty distinguishing pickup actions from hand movements that are guided by different intentions. If this is correct, then infants may more robustly represent the causal powers of other people who engage in simpler, albeit less familiar, efficient, object-directed actions. The next experiments test this possibility.

Experiments 3-5: Prereaching infants’ understanding of reaching actions that cause state changes in objects on contact

Experiment 3

Prereaching infants’ understanding of reaching actions that cause state changes in objects on contact

Drawing inspiration from past studies of infants’ and adults’ causal perception (12, 13, 38, 39, 45), in Experiment 3 we tested infants’ responses to displays similar to those of Experiments 1 and 2, except that the person reached for and touched the ball, causing it to illuminate on contact, and then withdrew her hand, causing the ball to return to its initial state. To minimize the familiarity of both the action and the causal outcome while maximizing both the attractiveness of the state change event and the simplicity of the contact relation between the hand and the object, the actor reached with a gloved hand, as in Experiment 1, and she touched the object with the tips of her fingers, whereupon a light and soft sound activated within the ball for as long as the actor touched it (Figure 1, H3-H4, T3). Because this event has not been used in previous research, infants were randomly assigned to one of two habituation conditions (N=40; 20 per condition; Mean age=108 days; range=91-122, 23 female). In the experimental condition, infants watched the person reach over a barrier that prevented direct access to the goal object (H3), as in Experiments 1 and 2. In the control condition, infants watched the person perform the same reaches with the barrier behind the goal object, out of the actor’s way, as in the control condition of previous research with mitten-trained infants (H4) (29). Across both conditions, all barriers were added digitally to the same videos: Thus, the actor performed identical actions in the two conditions, but only in the first condition did the actor appear to reach efficiently on the habituation trials. After habituation, infants viewed the efficient, direct reach and the inefficient, indirect reach, as in Experiments 1-2, both of which activated the object (T3). These two conditions allow us to test whether infants differentiate efficient from inefficient reaches at test only when prior curved reaches were efficient.

In Experiment 3, infants responded differently to the test events across the two habituation conditions ([0.273,0.732], ß=0.781, B=0.502, SE=0.114, p<.001, two-tailed).When the actor’s reaches were initially constrained by a barrier (H1) in the experimental condition, infants looked longer, at test, at the inefficient than the efficient action (Meanineff=15.448s, Meaneff=12.368s, [0.159,0.486], ß=0.501, B=0.322, SE=0.081, p<.001, two-tailed). Their preference for the inefficient test action cannot be attributed to low-level preferences for the curvilinear reach, because infants in the control condition (H2) showed a small preference in the opposite direction (Meanineff=8.788s, Meaneff=10.104s, [-0.343,-0.017], ß=-0.28, B=-0.18, SE=0.081, p=0.032, two-tailed). ). Infants’ preference for the inefficient action was stronger in this experiment than in Experiment 1, which presented the same reaching trajectories ending in object pickup ([0.029,0.467], ß=0.457, B=0.248, SE=0.112, p=0.032, two-tailed). Experiment 3 therefore provides evidence that infants are sensitive to the physical constraints on object-directed reaching when these reaches terminate in a simple, causally transparent contact event.

Experiment 4

In Experiment 4, pre-registered at https://osf.io/a5byn/, we tested whether this sensitivity depends on infants’ construal of the actor as a causal agent who changes the states of objects on contact. We introduced digital manipulations to the habituation and test events from Experiment 3 to create a small spatial and temporal gap between the termination of the actor’s reach and the activation of the object, thereby removing the key condition that elicits causal perception in older infants and adults (12, 13, 38, 39, 45). Infants (N=20; Mean age=107 days; range=93-121; 12 female) saw videos identical to those from the experimental condition of Experiment 3, except the actor’s hand never contacted the object (her fingers paused 50 pixels, or 2 cm, above it), and the object changed state 0.5 seconds after the hand came to rest in midair (H5, T4). In contrast to Experiment 3, infants looked equally at test trials showing the inefficient and efficient actions (Mineff=15.306s, Meff=16.38s, [-0.301,0.191], ß=-0.096, B=-0.055, SE=0.119, p=0.649, two-tailed). Across Experiment 4 (H5, T4) and the experimental condition of Experiment 3 (H3, T3), infants responded differently to the test events depending on whether or not the person acted on the object on contact ([0.003,0.623], ß=0.547, B=0.313, SE=0.154, p=0.049, two-tailed). Therefore, Experiment 3 provides initial evidence that infants appreciate the physical constraints on goal-directed reaching if this action causes a change in its goal object on contact, but not if the change in the object occurs after, and at a distance from, the end of the action.

Experiment 5

To evaluate this suggestion further, we conducted a pre-registered direct replication of Experiments 3 and 4. In Experiment 5, pre-registered at https://osf.io/f2hvd/, we randomly assigned infants to events that differed only in spatiotemporal continuity: the object either activated on contact with the agent’s hand, or after a small gap in space and time (N=52, 26 per condition; Mean age=107 days; range=92-121; 21 female). This design allowed us to compare infants’ responses to causal (H3, T3) versus non-causal (H5, T4) actions, under testing conditions where all researchers were blind to condition as well as test events. We fully replicated the findings from Experiments 3 and 4: Infants again responded to the test events differently depending on whether or not the activation of the object occurred on contact with the hand ([0.184,0.815], ß=0.729, B=0.5, SE=0.158, p=0.003, two-tailed). As in Experiment 3, infants looked longer at the inefficient than the efficient reach when the person appeared to cause a change in the object (Mineff=12.166s, Meff=7.791s, [0.211,0.66], ß=0.635, B=0.435, SE=0.112, p<.001, one-tailed); as in Experiment 4, infants looked equally to the inefficient and efficient reaches when she did not appear to cause this outcome(Mineff=11.395s, Meff=12.888s, [-0.289,0.16], ß=-0.094, B=-0.064, SE=0.112, p=0.567, two-tailed). Although 3-month-old infants have limited experience acting on objects themselves, they understand that other people intend to cause changes in the world through their actions. Infants exhibited this ability in Experiments 3 and 5, both of which presented clear information that a change in the goal object occurred on contact with the actor’s hand.

Main text report of meta-analysis

To explore these effects further and compare them to past research using the same method at the same age (29), we performed a meta-analysis over ten experiments (Experiments 1-5, and all experiments from Skerry et al. (29); total N=264; see Fig S1). The magnitude of infants’ looking preference to the indirect versus direct reach was greater after mittens training, relative to no training ([0.029,0.074], ß=0.583, B=0.052, SE=0.011, p<.001, two-tailed), as demonstrated in past training studies (27, 28, 31, 32). Infants also showed a stronger preference for the indirect reach when the actor simply touched an object and caused a change in its state than when she lifted and displaced the object ([0.011,0.042], ß=0.302, B=0.027, SE=0.008, p=0.001, two-tailed). Most importantly, infants’ looking preference was stronger when these actions occurred on contact, rather than at a distance and after a delay ([0.025,0.058], ß=0.467, B=0.041, SE=0.009, p<.001, two-tailed). Knowledge of the causal intentions behind and physical constraints on reaching actions therefore arises without training, but it is more robust when infants view causally transparent actions or receive mittens training. For full meta-analytic methods and results, see SI Appendix.

Reliability (Methods Section)

To assess reliability, 50% of test trials from participants across Experiments 1-5 (76 participants, 456 trials) were randomly selected and coded by additional researchers who were unaware of experimental condition, and test trial order. The intraclass correlation coefficient (ICC) between the original data, and this newly coded data, was 0.969 [0.946, 0.982], 0.969 [0.943, 0.982], 0.968 [0.955, 0.978], 0.963 [0.938, 0.977], 0.936 [0.911, 0.954], for Experiments 1 through 5, respectively.

Supplementary Results

Comparing results including and excluding influential participants.

Across all of our experiments, we checked for influential participants in every model using Cook’s Distance (69), as stated in the main text. This is a method for outlier detection: The purpose of this step in our analysis is to identify individuals whose inclusion in the analysis may have undue influence by either masking the effect, which is otherwise present across the rest of the sample, or by driving the effect, which is otherwise absent across the rest of the sample. Below are the results from the main text detailing how many influential participants were detected in each analysis, and report the results including these participants. Overall, none of the main conclusions reported in the main text differ depending on the inclusion or exclusion of these participants (though see below for a minor difference in the findings from Experiment 2, and the analysis collapsing across Experiment 1 and Skerry et al. (2013)).

In the primary analysis for Experiment 1, we detected one influential participant. Including this participant in the analysis generates the same finding as reported in the main text: Infants looked equally at the efficient vs inefficient reach of a gloved hand ([-0.169,0.209], ß=0.041, B=0.02, SE=0.092, p=0.831, two-tailed). In the analysis comparing Experiment 1 to Skerry et al. (2013) Experiment 3, we detected 2 influential participants. Including them results in a null difference between these two experiments ([-0.086,0.415], ß=0.279, B=0.165, SE=0.128, p=0.205, two-tailed). This difference does not change our interpretation of Experiment 1: Infants do not appear to respond to the efficiency of pickup actions when the person reaching wears a glove or a mitten.

In the primary analysis for Experiment 2, we detected 2 influential participants. Including them in the sample generates a marginal effect in the same direction as that reported in the main text: Infants looked longer at the inefficient than the efficient reach of a bare hand ([-0.024,0.318], ß=0.297, B=0.147, SE=0.083, p=0.091, two-tailed). In the analysis comparing Experiment 2 to Skerry et al. (2013) Experiment 3, we detected 1 influential participant. Including them results in the same finding as reported in the main text: Infants’ looking preferences significantly differed across these two experiments ([0.048,0.536], ß=0.495, B=0.292, SE=0.121, p=0.021, two-tailed). These findings do not change our conclusion in the main text: Experiments 1 and 2 overall show that infants have inconsistent, fragile expectations about the efficiency of reaches that result in displacing objects.

In the analysis collapsing across Experiments 1 and 2, we found 1 influential participant. Inclusion of that participant generates a null effect ([-0.042,0.209], ß=0.139, B=0.083, SE=0.063, p=0.191, two-tailed), whereas in the main text this effect was marginal, but our conclusion is the same: Infants do not show robust sensitivity to the cost of reaching actions when these actions result in objects being displaced. In the analysis comparing infants’ looking preferences across Experiments 1 and 2, we found 3 influential participants, and including them results in the same result as reported in the main text: Infants’ looking preferences did not differ across the two experiments, ([-0.116,0.37], ß=0.211, B=0.127, SE=0.124, p=0.311, two-tailed).

In the primary analysis for Experiment 3, we detected 2 influential participants. Including them in the sample generates the same finding as reported in the main text: Infants’ looking preferences for the test events differed as a function of whether they were habituated to constrained action over a barrier (experimental group) or the same actions not over a barrier (control group) ([0.115,0.657], ß=0.596, B=0.502, SE=0.114, p<.001, two-tailed). In the experimental condition, infants looked longer at the inefficient action ([0.065,0.451], ß=0.398, B=0.258, SE=0.095, p=0.01, two-tailed). In the control condition, infants looked equally at the two test actions ([-0.321,0.065], ß=-0.198, B=-0.128, SE=0.095, p=0.186, two-tailed).

We did not detect any influential participants in the analyses for Experiments 4 and 5.

Comparing bare hands, gloves, and mittens

Because Experiments 1 and 2 used the methods of Skerry et al. (2013), the primary difference between the events from Skerry et al. (2013) (SCS), and Experiments 1 and 2 from the main text concerned the presentation of the reaching hand, which was bare in Experiment 2, covered by tight-fitting gloves in Experiment 1, and covered by thick mittens in SCS, as in all the prior published research involving mittens training. Could infants’ responses to the reaches from these experiments be explained, in part, by how easy it was to see the configuration of the hand (easy in Experiment 2, slightly harder in Experiment 1, and even harder in SCS)? To explore this question, we analyzed infants’ proportion looking to the inefficient action in Experiment 1, Experiment 2, and the comparable experiment from SCS where infants had no mittens training (SCS Experiment 3), and asked whether the clarity of the person’s hand in each of these experiments (2 in Experiment 2, 1 in Experiment 1, and 0 in SCS Experiment 3) predicted differences in looking preferences, controlling for correlated data within experiments. This analysis revealed that infants’ sensitivity to the efficiency of this reach increased with increasingly clear information about the form of the hand ([0.007,0.053], ß=0.416, B=0.03, SE=0.011, p=0.011, two-tailed, excluding 4 influential participants). This finding held regardless of whether the influential participants were excluded or included (in the latter case, [0.005,0.053], ß=0.359, B=0.029, SE=0.012, p=0.02, two-tailed). ## Meta-analytic results

To assess the effects of our experimental manipulations in Experiments 1-5 and in Skerry et al. (29), we performed an analysis over these two papers (total N=264, 12 conditions). Our analytic approach allows us to assess the independent effects of 5 manipulations: the type of or absence of motor training, the presence or absence of a barrier preventing a direct reach for the object during habituation, the nature of the goal (to change the state of an object or pick it up), the presence or absence of action on contact, and the presence or absence of mittens on the actor. The analysis also allows us to control for the participant variables of age and sex, and model the nested structure of the data (e.g. looks clustered within experiments and within papers). For ease of interpretation, we used average proportion looking to the inefficient action in this analysis, following Skerry et al. (29). The findings below exclude 16 participants on the basis of Cook’s Distance, leaving 248 infants in the final sample. See Table S1 for results including all participants.

This analysis confirmed the findings from the individual experiments reported in the main text and in Skerry et al. (28): Infants’ expectations were stronger when the observed action was spatiotemporally continuous with its effect (i.e., appeared to be causal), [0.025,0.058], ß=0.467, B=0.041, SE=0.009, p<.001, two-tailed, when infants received effective motor training (sticky mittens), relative to no training [0.029,0.074], ß=0.583, B=0.052, SE=0.011, p<.001, two-tailed, when the observed agent’s actions were constrained by a barrier and were efficiently adapted to that barrier, relative to the same actions that were unconstrained by a barrier, [0.021,0.051], ß=0.406, B=0.036, SE=0.008, p<.001, two-tailed, and when the agent pursued a state change goal, relative to a pickup goal, [0.011,0.042], ß=0.302, B=0.027, SE=0.008, p=0.001, two-tailed. We also found that infants’ expectations were marginally negatively affected when they received ineffective motor training (non-sticky mittens), relative to no training, [-0.058,0], ß=-0.33, B=-0.029, SE=0.015, p=0.051, two-tailed, and improved as the form of the hand became clearer [0.003,0.056], ß=0.333, B=0.03, SE=0.013, p=0.027, two-tailed, but neither of the latter two findings was present in the full analysis with all participants (see Table S1). These findings provide further evidence that action experience alters action interpretation, but so does causal information and information about efficiency.

Figure S1. Figure S1. (A) Proportion looking towards the inefficient reach and (B) looking time in seconds towards the efficient versus inefficient reach, and at test across Experiments 1-5 (n=152) and across Experiments 1-5 in Skerry et al. (SCS) (29) (n=112). Labels above each panel list the experiment name (Exp. 1-5, SCS Exp. 1-5), type of motor training (none, ineffective non-sticky mittens, or effective sticky mittens), whether actions during habituation were constrained or unconstrained by a barrier, goal (state.change or pick.up), whether actions resulted in contact with the object, whether the actor reached with a bare, gloved, or mittened hand, and video displays listed in Figure 1. Error bars around means indicate within-subjects 95% confidence intervals (B) and bootstrapped 95% confidence intervals (A). Individual points (A) or pairs of connected points (B) indicate data from a single participant. Horizontal bars within boxes indicate medians, and boxes indicate the middle 2 quartiles of data. Violin plots (A) indicate distribution of data, area scaled proportionally to the number of observations. All data and analyses are open source and available at https://osf.io/rcsns/.

Figure S2.. Effect plots for model investigating predictors of sensitivity to action efficiency across Experiments 1-5 and Skerry et al. (29) (total N=264, 248 included in the final analysis, 16 excluded on the basis of Cook’s Distance). Each point shows estimates of effects at each level of all predictors: Type of motor training (none, ineffective non-sticky mittens, or effective sticky mittens), the goal of the actor (state change vs pick up), action during habituation (constrained or unconstrained by a barrier), whether actions resulted in contact with the object (yes or no), and the clarity of the form of the hand (0=mittens, 1=gloves, 2=bare hand). Error bars indicate 95% confidence intervals. See Table S1 for full results.



Table S1. (A) Regression table for model investigating predictors of sensitivity to action efficiency across Experiment 1-5 and all experiments from Skerry et al. (29) (total N=264, 248 included in final analysis, 16 excluded on the basis of Cook’s Distance). (B) Regression table for the same analysis, including all participants. Dependent measure is proportion looking towards the inefficient reach, averaged across 3 test trials during test. Categorical predictors were coded using sum contrasts, and fixed effects from the model should therefore be interpreted with respect to the grand mean. Model formula prop.ineff.all ~ training + goal + hab + causal + mitten + (1|experiment) + (1|ageday) + (1|sex) + (1|paper).

beta b se df t p lower upper
(Intercept) -0.716 0.457 0.012 241 37.17 0.000 0.433 0.481
effective training 0.583 0.052 0.011 241 4.50 0.000 0.029 0.074
ineffective training -0.330 -0.029 0.015 241 -1.96 0.051 -0.058 0.000
state change goal 0.302 0.027 0.008 241 3.39 0.001 0.011 0.042
reach constrained by barrier 0.406 0.036 0.008 241 4.67 0.000 0.021 0.051
action on contact 0.467 0.041 0.009 241 4.86 0.000 0.025 0.058
clarity of hand 0.333 0.030 0.013 241 2.22 0.027 0.003 0.056
beta b se df t p lower upper
(Intercept) -0.640 0.455 0.016 10.73 28.34 0.000 0.424 0.487
effective training 0.578 0.058 0.015 7.55 3.79 0.006 0.028 0.088
ineffective training -0.355 -0.035 0.019 7.58 -1.86 0.102 -0.073 0.002
state change goal 0.301 0.030 0.011 6.75 2.79 0.028 0.009 0.051
reach constrained by barrier 0.350 0.035 0.010 17.43 3.61 0.002 0.016 0.054
action on contact 0.423 0.042 0.010 37.41 4.11 0.000 0.022 0.062
clarity 0.294 0.029 0.018 7.48 1.66 0.137 -0.005 0.064

Exclusion info

Table S2. Tally of infants who participated in Experiments 1-5 but were excluded in our final sample. These exclusion criteria vary slightly across experiments (e.g. we relaxed our definition of inattentiveness from excluding all data from a participant if they missed a test trial in Experiment 1, to excluding data from just that trial in Experiments 2-5).

Experiment Fussiness Inattentiveness Caregiver Interference Experimenter/Coding Error Technical Failure Total
Exp.1 7 0 0 2 0 7
Exp.2 6 0 0 1 2 9
Exp.3 9 5 1 12 3 30
Exp.4 0 0 0 2 0 2
Exp.5 6 0 0 2 0 8
Total 28 5 1 19 5 50

Distribution of Looks

Figure S3. Density plot of looking times during test across Experiments 1-5 from the present research (Liu, Brooks, and Spelke; LBS, left panel), and Experiments 1-5 from Skerry et al. (2013) (SCS, right panel) (N=264). Maximum-likelihood fitting revealed that the lognormal distribution (log likelihood=-1720.509) provides a better fit to these data than the normal distribution (log likelihood=-1842.196).


Attention during habituation across Exp 1-5

Figure S4. Total looking time in seconds during habituation across Experiments 1-5. Error bars around means indicate bootstrapped 95% confidence intervals (CIs). Individual points indicate data from a single participant. Horizontal bars within boxes indicate medians, and boxes indicate the middle 2 quartiles of data. Violin plots in indicate distribution of data, area scaled proportionally to the number of observations.


To ask whether infants’ total attention during habituation was affected by experimental manipulations across Experiments 1-5 (action constrained vs unconstrained by a barrier, state change vs pickup goal, mittened, gloved, or bare-handed actor, and action with vs without contact with the object), and varied by gender and age, we fit a mixed effects model on these fixed effects and experiment (1-5) as a random intercept. We found that the only robust predictor of attention during habituation was age, [-3.4,-0.714], ß=-0.233, B=-2.058, SE=0.68, p=0.003, two-tailed, such that older infants looked for a shorter time overall than younger infants.

Figure S5. Looking time in seconds during each habituation trial across Experiments 1-5. Curves with 95% confidence interval ribbons indicate smoothed conditional means, generated using the loess method. Connected points indicate data from a single participant. Labels above each panel list the experiment name (Exp. 1-5), whether actions during habituation were constrained or unconstrained by a barrier, goal (state.change or pick.up), whether actions resulted in contact with the object, whether the actor reached with a mittened, gloved, or bare hand, and video displays listed in Figure 1.


Table S3 Regression table for mixed effects model analyzing the effect of age, sex, order of test events, habituation condition, goal, coverage of the hand, and causal information on total looking time habituation, controlling for other variations across Experiments 1-5. Model formula: total_hab ~ ageday + sex + first.test + hab + goal + clarity + causal + (1|experiment).

beta b se df t p lower upper
(Intercept) 0.171 373.160 89.49 51.41 4.170 0.000 194.14 553.006
Age in Days -0.233 -2.058 0.68 147.54 -3.026 0.003 -3.40 -0.714
Sex 0.066 5.203 6.11 148.65 0.852 0.396 -6.92 17.274
First Test Event -0.006 -0.439 6.00 146.65 -0.073 0.942 -12.27 11.393
Habituation 0.222 17.590 11.03 131.57 1.595 0.113 -6.44 41.220
Goal 0.007 0.589 16.02 6.18 0.037 0.972 -37.44 37.615
Clarity of hand -0.253 -19.993 38.05 5.73 -0.525 0.619 -110.17 70.275
Action on Contact -0.055 -4.379 9.08 75.38 -0.482 0.631 -23.75 13.935

Three-month-old infants appreciate that other people’s reaching actions are causal, goal-directed, and physically constrained without experiencing reaching for objects themselves.